Inverse Function Theorem

1. Oct 11, 2006

Haftred

I'm trying to see near which points of R^3 I can solve for theta, phi, and rho in terms of x,y, and z. I know i need to find the determinant and see when it equals zero; however, I get the determinant to equal zero when sin(phi) = 0, and when tan(theta) = -cot(phi). The first is right, but i've checked my work many times and keep getting the last solution. I just calculated the determinant of the partial derivatives (dx/dtheta, dx / dphi, dx / drho...dy/dtheta, dy/dphi, dy/drho...dz/dtheta, dz/dphi, dz/drho). I've checked my work many times. Am I correct, or am I doing something wrong?

2. Oct 11, 2006

StatusX

That doesn't look right. What is the equation you got for the determinant?

3. Oct 11, 2006

Haftred

p = rho
a = phi
b = theta

p^2[cos(a)sin(a)(cosb)^3 + (sina)^2(sinb)^3 + cos(b)cos(a)sin(a)(sinb)^2 + sin(b)(sina)^2(sinb)^2].

I differentiated with respect to rho in the first column, phi in the second column, and theta in the third.

Thanks.

4. Oct 11, 2006

StatusX

I get something different. All I can suggest is go back through it carefully.

5. Oct 11, 2006

Haftred

thanks statusx for your time..i appreciate it